Hopf bifurcations of a ratio-dependent predator–prey model involving two discrete maturation time delays
| Autor: | Esra Karaoglu, Hüseyin Merdan |
|---|---|
| Přispěvatelé: | TOBB ETU, Faculty of Science and Literature, Depertment of Mathematics, TOBB ETÜ, Fen Edebiyat Fakültesi, Matematik Bölümü, Merdan, Hüseyin |
| Rok vydání: | 2014 |
| Předmět: |
System
Hopf bifurcation Period-doubling bifurcation General Mathematics Applied Mathematics Mathematical analysis Differentıal Equations General Physics and Astronomy Statistical and Nonlinear Physics Saddle-node bifurcation Functional-Response Bifurcation diagram Biological applications of bifurcation theory symbols.namesake Pitchfork bifurcation Neural-Network Model symbols Stability Center manifold Bifurcation Mathematics |
| Zdroj: | Chaos, Solitons & Fractals. 68:159-168 |
| ISSN: | 0960-0779 |
| DOI: | 10.1016/j.chaos.2014.07.011 |
| Popis: | In this paper we give a detailed Hopf bifurcation analysis of a ratio-dependent predator prey system involving two different discrete delays. By analyzing the characteristic equation associated with the model, its linear stability is investigated. Choosing delay terms as bifurcation parameters the existence of Hopf bifurcations is demonstrated. Stability of the bifurcating periodic solutions is determined by using the center manifold theorem and the normal form theory introduced by Hassard et al. Furthermore, some of the bifurcation properties including direction, stability and period are given. Finally, theoretical results are supported by some numerical simulations. (C) 2014 Elsevier Ltd. All rights reserved. TUBITAK (Scientific and Technological Research Council of Turkey) |
| Databáze: | OpenAIRE |
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